Update
Azure Functions need to access on-prem MS SQL Databases via Azure Managed Identity.
Does Azure Managed Identity support this?
Update
Managed identities allows Azure resources to authenticate or authorize themselves with other supported Azure resources.
On-Premise MS SQL Server supports two authentication modes, Windows authentication mode and mixed mode.
Azure Managed Identity does not support your case - Azure Function connection to On-Premise MS SQL Server.
Update June 2024: In SQL Server 2022 Microsoft introduced support for Microsoft Entra authentication